Solve for $x$ and $y$ using elimination. ${6x-y = 48}$ ${5x+y = 51}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-y$ and $y$ cancel out. $11x = 99$ $\dfrac{11x}{{11}} = \dfrac{99}{{11}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {6x-y = 48}\thinspace$ to find $y$ ${6}{(9)}{ - y = 48}$ $54-y = 48$ $54{-54} - y = 48{-54}$ $-y = -6$ $\dfrac{-y}{{-1}} = \dfrac{-6}{{-1}}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {5x+y = 51}\thinspace$ and get the same answer for $y$ : ${5}{(9)}{ + y = 51}$ ${y = 6}$